Emerging Applications of Algebraic Geometry pp 271-324
Positivity and Sums of Squares: A Guide to Recent Results
This paper gives a survey, with detailed references to the literature, on recent developments in real algebra and geometry concerning the polarity between positivity and sums of squares. After a review of foundational material, the topics covered are Positiv- and Nichtnegativstellensatze, local rings, Pythagoras numbers, and applications to moment problems.
Key wordsPositive polynomials sums of squares Positivstellensatze real algebraic geometry local rings moment problems
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